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Search: id:A129155
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| A129155 |
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Number of skew Dyck paths of semilength n that have no primitive Dyck factors. A skew Dyck path is a path in the first quadrant which begins at the origin, ends on the x-axis, consists of steps U=(1,1)(up), D=(1,-1)(down), and L=(-1,-1)(left) so that up and left steps do not overlap. The length of the path is defined to be the number of its steps. A primitive Dyck factor is a subpath of the form UPD that starts on the x-axis, P being a Dyck path. |
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+0
2
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| 1, 0, 1, 4, 15, 59, 241, 1011, 4326, 18797, 82685, 367410, 1646494, 7432270, 33761322, 154213566, 707882503, 3263713148, 15107319268, 70182332975, 327111450097, 1529226524057, 7168880978609, 33693179852563
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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a(n)=A129154(n,0).
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REFERENCES
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E. Deutsch, E. Munarini, and S. Rinaldi, Skew Dyck paths (in preparation).
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FORMULA
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G.f.=[3-3z-sqrt(1-6z+5z^2)]/[2+z-sqrt(1-4z)+sqrt(1-6z+5z^2)].
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EXAMPLE
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a(3)=4 because we have UUUDLD, UUDUDL, UUUDDL, and UUUDLL.
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MAPLE
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G:=(3-3*z-sqrt(1-6*z+5*z^2))/(2+z-sqrt(1-4*z)+sqrt(1-6*z+5*z^2)): Gser:=series(G, z=0, 32): seq(coeff(Gser, z, n), n=0..28);
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CROSSREFS
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Cf. A129154, A129157.
Adjacent sequences: A129152 A129153 A129154 this_sequence A129156 A129157 A129158
Sequence in context: A128714 A007342 A017951 this_sequence A070071 A007161 A007167
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 02 2007
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